This article is the third in a series on possible ways to use mathematics to cure or treat cancer, that began with Can Mathematics Cure Cancer?. It presents the Bathtub Mechanism, a possible way to kill cells with abnormal numbers of chromosomes, a common characteristic of many cancer cells, in greater detail and presents several animations of the mechanism.

Cancer is the second leading cause of death in the United States. Over five-hundred thousand people died from cancer in 2007. If current trends continue, about one in three of readers will die from cancer.

Since 1971 the United States has spent about $200 billion on research into cancer. The National Cancer Institute has an annual budget of over $5 billion. This is comparable to the Manhattan Project that invented the atomic bomb and the first nuclear reactors continued for forty years. The results have clearly been quite disappointing. Is there a way to get better results from the many years of hard work, billions of dollars, and mountains of knowledge collected? Are there ways to apply today’s powerful computers and mathematics to defeat this disease?

Cancer is now thought to be caused by mutations of genes, cancer genes or oncogenes and tumor suppressor genes, that control complex networks of proteins that regulate the division, growth, and differentiation of cells in the body. Differentiation refers to the process by which cells turn into specialized kinds of cells such as skin, blood, and nerves. As we age, we accumulate mutations of these genes in some cells. It requires several mutations of several different genes to produce most forms of cancer. Many different sets of mutated genes cause cancer.

While a medical doctor or pathologist may identify a cancer as breast cancer or skin cancer, at a molecular and genetic level, skin cancer is thought to be many different cancers caused by many different sets of mutated genes. In total, cancer is now thought to be thousands of different diseases. This makes finding a single chemical similar to penicillin, for example, that can kill all cancers either impossible or very difficult, at least by starting from the individual cancer genes and the proteins they produce.

Even worse, cancer cells are generally thought to become genetically unstable and mutate much more rapidly than normal cells. Hence, the cancer cells begin to evolve in the body and can develop immunity to anti-cancer drugs such as chemotherapy agents.

While cancer varies enormously at the level of genes and proteins, the part level, cancer cells may have common system-level features. For example, pathologists can identify cancer cells or tissues from biopsies under an optical microscope as cancer. Another common characteristic is that many, perhaps all, cancer cells have an abnormal number of chromosomes, often too many. This article considers targeting the abnormal number of chromosomes.

The Bathtub Mechanism, developed by the author several years ago, is an algorithm, which can be implemented by a relatively simple set of molecules, that may be able to selectively destroy cell with an abnormal number of chromosomes. This system of drugs is like a bathtub with several running faucets, one for each chromosome, and a single drain. If there are too many faucets, chromosomes, the water level, the concentration of the cell killer, will rise and overflow the bathtub. If there are the right number, forty-six, or too few, less than forty-six, faucets, the drain can remove the water being added and the water level never rises. The water level remains almost zero; the concentration of the cell killer is far too low to harm the cell.

One can kill cells with too few chromosomes (less than forty-six) by swapping the roles of the drain and the source. The drain is now a feature of the chromosomes. The source is the constant numerical feature of the cells. Thus, if there are too few chromosomes, there are not enough drains to remove the cell killer produced by the source. The bathtub has one big faucet and many small drains, one for each chromosome. The water level, the concentration of the toxin, rises if there are too few drains/chromosomes.

It may be possible to create proteins that react directly with the source and drain features in the cell. On the other hand, it may be necessary to use a source and a drain catalyst that bind to the source and drain features and become active catalysts only when binding to the source or drain features. In this article the first case is considered. The source and drain catalysts are discussed in more detail in the previous two articles.

D Drain
IS Inhibitor Source
S Source (on or associated with chromosome, may be a DNA sequence)

The bathtub mechanism requires two features in the cell: a numerical or quantitative feature that is proportional to the number of chromosomes and a feature that is constant in all cells, both normal and cancerous. Some obvious features that probably vary with the number of chromosomes are the telomeres at the end of the chromosomes and the centromeres at the center of the chromosomes.

There are many molecular structures in the chromosomes and associated with the chromosomes. It seems probable, although not certain, that one can find a numerical or quantitative feature that varies with the number of chromosomes that could be used. A more serious problem with the bathtub mechanism is the constant feature that is the same in both healthy cells and cancer cells, especially since cancer cells are thought to be constantly mutating and changing. This may be a show-stopper.

Since the cancer cells may be mutating, it may be impossible to find a constant feature in the cancer cells. The feature could disappear entirely or change in size or number. There is at least one possible way to add such a feature artificially to the cells, both healthy and malignant.

A bacteriophage is a kind of virus that attaches to the exterior membrane of a cell and injects its genetic material into the cell. The bacteriophage’s genetic material then takes over the machinery of the cell and directs it to make more bacteriophages. The bacteriophage consists of a protein sheath that looks something like a science fiction bug with several arms (see animations below) that grab the surface of the cell and a spherical or polyhedral chamber that carries the genetic material.

In principle, one could modify the genetic material of the bacteriophage to create cells (the commonly used E. Coli bacteria, for example) that make not the virus, but the protein sheath with a payload of other proteins or non-coding DNA sequences, in particular DNA sequences that regulatory proteins bind to. These pseudo-bacteriophages would inject their protein or non-coding DNA payloads into cells instead of the genetic material of the naturally occurring bacteriophage. They would not be infectious like a normal virus.

If, and this is a big if, one could modify the protein sheath so it would only inject the protein or non-coding DNA payload into a cell without an inhibitor protein I that is generatd by inhibitor sources (IS) in the payload, one could inject a payload that contained an artificial constant drain feature D and the inhibitor sources IS into the cell. The inhibitor protein I might work, for example, by blocking the arms of the bacteriophage from attaching to the exterior membrane of the cell, which presumably triggers the injection of the payload.

Once the new drain feature was added to the cell, the pseudo-bacteriophages would stop injecting payloads into the cell because it now also contained the inhibitors. Thus, a constant number of features could be added to each cell, both healthy and cancerous.

The Pseudo-Bacteriophage Payload is either a string of protein units or non-coding DNA with repeated sequences of regulatory protein binding sites, drains D and inhibitor sources IS

The inhibitor I and the inhibitor source IS are represented by the blue spheres in the payload string

The drain D is the orange spheres in bacteriophage payload

The bacteriophage payload is shown as a string of blue and orange spheres in the first four animations below, mostly clearly in the fourth closeup animation. The inhibitors are shown in the second animation as blue spheres on the surface of the cell that prevent the bacteriophage from injecting a second payload string (drain) into a cell.

The payload is a single strand of protein sub-units or non-coding DNA. When the cell divides, the payload should end up in only one daughter cell. The other daughter cell will lack the payload and the inhibitor sources. The pseudo-bacteriophages will then add another payload string with the drain to the drainless daughter cell.

Alternatively, if the payload is a non-coding DNA string, not proteins, it may be possible to integrate the DNA string into the cell’s DNA, the chromosomes, as a single inherited drain. In this case, the drain will be inherited by both daughter cells when the cell divides.

Animations

The following animations illustrate the Bathtub Mechanism, a basic concept. The animations were created by the author using the free POV-Ray (Persistence of Vision Ray Tracing Program) for Windows 3.62 on a PC running Windows XP Service Pack 2. The POV-Ray scene description files contain a very simple mathematical model of the bathtub mechanism. The rendered frames were combined into MPEG-4 video files using the free, open-source ffmpeg video encoding utility. These animations illustrate a basic concept. They are not a quantitative mathematical model or simulation of cells, even at low fidelity.

This animation shows a pseudo-bacteriophage injecting a drain payload into a cell:

This animation shows a pseudo-bacteriophage prevented from injecting a second drain payload into a cell that already has a drain. The blue spheres are the inhibitors that prevent the pseudo-bacteriophage legs from attaching to the cell membrane.

This animation shows a wide angle view of the harmless precursor (red cone with green sphere cap) converted to the cell killer (red cone) by the telomere (yellow end of cylinder) of a single chromosome and then neutralized by the drain payload (shown as a string of orange drain spheres and blue inhibitor source spheres):

This animation shows a closeup view of the harmless precursor (red cone with green sphere cap) converted to the cell killer (red cone) by the telomere (yellow end of cylinder) of a single chromosome and then neutralized by the drain payload (shown as a string of orange drain spheres and blue inhibitor source spheres):

This animation shows a normal cell with forty-six chromosomes (represented by a simple blue sphere for clarity). The drain is represented by a simple green and gray sphere for clarity. The drain is green when it can process a cell killer, converting it to a harmless fragment (represented by a white sphere for clarity) which is excreted by the cell. The drain is black when it is processing a cell killer and cannot convert another. The drain has a maximum throughput. In a normal cell, the drain can remove as many cell killers as are added by the sources, the chromosomes. The concentration of the cell killer, the number in the lower right corner of the animation, remains low, never reaching the lethal level of two-hundred.

This animation shows the cell killer concentration rising and killing a cancer cell with too many chromosomes (represented by two blue spheres for two sets of chromosomes). The cell killer concentration is the number displayed in the lower right corner. The drain cannot remove the cell killers as rapidly as they are added. The concentration rises to the lethal level of two-hundred and the cell disintegrates. The membrane is shown decaying by making it more and more transparent as the cell killer concentration rises.

Future Steps

Many technical details and difficulties have been omitted to present the idea. While it might be possible to research and develop the bathtub mechanism entirely empirically at a laboratory bench through extensive trial and error, it should be possible to substantially accelerate the development process by simulating the molecular mechanisms using today’s powerful computers. In practice, it would probably require careful tuning of the chemical reaction rates in the cell to produce the desired selective destruction of cells with abnormal numbers of chromosomes or other features associated with cancer.

The next logical step is to construct a mathematical model and simulation of the bathtub mechanism in real cells, iteratively increasing the level of fidelity. This would enable evaluation of the feasibility of the concept and of specific variants of the concept, as many variations are possible and more will become evident with detailed simulation and working through of the concept. Perhaps more importantly a detailed simulation would make it easier for specialists in various fields of biology and organic chemistry — chromosomes, bacteriophages, proteins, many others — to see where their expertise could fit into the concept or resolve otherwise intractable problems.

Naturally occurring networks of proteins and other molecules in cells seem to be able to perform many complex mathematical and logical calculations, such as the feedback control networks that seem to malfunction in cancer. While one cannot be certain, it is not unlikely that a relatively simple network of proteins and other molecules can implement the bathtub mechanism or something similar.

Even engineering a single molecule such as genetically engineered insulin for diabetics is a daunting task at present. So a system of even a few molecules would be a substantial and difficult undertaking. Nonetheless it is probably doable now or in the near future.

However, the underlying biology is unknown. Even though there are over one-million research papers on cancer, it is difficult to get a clear picture of the role of aneuploidy in cancer. Most modern cancer research is conducted within the framework of the oncogene theory and an implicit assumption that the way to cure or treat cancer is to target either a protein generated by a cancer gene or the gene directly.

Chromosomal anomalies, both abnormal numbers of chromosomes and the rearrangements of chromosomes that are common in many cancers, are usually discussed as an aside to the putative cancer genes. This translocation of chromosome X mutated the key cancer gene ABC, or the duplication of chromosome X resulted in two copies of the key cancer gene ABC.

It could be that killing cancer cells with the wrong number of chromosomes would have no effect on the disease. It would simply result in a cancer with the correct number of chromosomes in the surviving cancer cells. It could slow the disease if the abnormal number of chromosomes is related to the malignancy of the cancer cells. In the best case, it might cure the disease, if the abnormal number of chromosomes is either the cause of cancer or essential in some way to the malignant characteristics of the cancer cells.

Conclusion

Everyone faces about a one in three chance of dying from cancer. Cancer researchers would like more impressive results to show policy makers and the general public, especially when seeking continued or increased funding. Pharmaceutical and biotechnology companies should desire improved anti-cancer drugs and treatments to maintain and increase their profits. Defeating cancer would free up resources and researchers to tackle other diseases of old age and even the aging process itself.

It may be possible to cure or effectively treat cancer with a system of smart drugs that perform a simple mathematical or logical calculation to selectively destroy cancer cells or probable cancer cells while sparing most normal healthy cells. These systems of smart drugs may be able to identify system level features of cancer cells independent of the confusing plethora of cancer genes and tumor suppressor genes.

The bathtub mechanism discussed in this article is one possible example of such a system of smart drugs. Mathematics and computers can enable or greatly accelerate the development of such systems of smart drugs.

Given the multitude of cancer genes and tumor suppressor genes that have been discovered in the last forty years, we should look at other aspects of cancer such as possible system level features for a cure or effective treatment. Today’s powerful computers, mathematics, and physics combined with the vast biological knowledge acquired in the last forty years may make it possible to attack cancer successfully in ways that were not practical even a few years ago.

John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing video compression and speech recognition technologies. He has extensive experience developing software in C, C++, Visual Basic, Mathematica, MATLAB, and many other programming languages. He is probably best known for his AVI Overview, an Internet FAQ (Frequently Asked Questions) on the Microsoft AVI (Audio Video Interleave) file format. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech). He can be reached at jmcgowan11@earthlink.net.

14 Responses to “Animations of a Possible Cure for Cancer”

I received a comment that bacteriophages attack bacteria and not mammalian (e.g. human) cells. As stated, this article omits a number of technical details and difficulties in order to illustrate the basic concept simply and clearly.

The author is not a biologist. It would probably take a collaboration among several different types of biologists, organic chemists, mathematicians, and physicists to successfully implement the bathtub mechanism.

With respect to bacteriophages, there has been research on modifying bacteriophages to inject genes into mammalian (e.g. human) cells. See, for example, this article:

We have genetically modified filamentous bacteriophage to deliver genes to mammalian cells. In previous studies we showed that noncovalently attached fibroblast growth factor (FGF2) can target bacteriophage to COS-1 cells, resulting in receptor-mediated transduction with a reporter gene. Thus, bacteriophage, which normally lack tropism for mammalian cells, can be adapted for mammalian cell gene transfer. To determine the potential of using phage-mediated gene transfer as a novel display phage screening strategy, we transfected COS-1 cells with phage that were engineered to display FGF2 on their surface coat as a fusion to the minor coat protein, pIII. Immunoblot and ELISA analysis confirmed the presence of FGF2 on the phage coat. Significant transduction was obtained in COS-1 cells with the targeted FGF2-phage compared with the nontargeted parent phage. Specificity was demonstrated by successful inhibition of transduction in the presence of excess free FGF2. Having demonstrated mammalian cell transduction by phage displaying a known gene targeting ligand, it is now feasible to apply phage-mediated transduction as a screen for discovering novel ligands.—Larocca, D., Kassner, P. D., Witte, A., Ladner, R. C., Pierce, G., Baird, A. Gene transfer to mammalian cells using genetically targeted filamentous bacteriophage.

I also received a comment that the telomeres and centromeres vary in size and geomtry from cell to cell, raising questions about how to “count” the chromosomes using these features.

In the case of the telomeres, the telomeres are supposed to consists of repeating sequences of DNA such as:

(repeat)(repeat)(repeat)….(repeat)(repeat)(repeat)(end of chromosome)

In the usual explanations, each time the cell divides, one repeat sequence is discarded, in principle until the cell has divided a maximum number of times and the cell (a normal cell) will die. This is the basis of the claims linking the telomeres to the aging prcoess. Thus, the size of the telomere varies with the age of the cells and possibly other factors.

If the non-toxic precursor (A(BC)) in the bathtub mechanism is engineered to react with the end of the telomere:

I use tentative language such as “supposed” intentionally. Many features of cells and chromosomes are inferred by indirect means. Optical microscopes have a maximum resolution of about 250 nanometers which is much larger than many of the features or molecular building blocks under discussion.

Similarly, with other recognized features of the chromosomes such as the centromeres, it may be possible to use a beginning, end, or edge of the feature to “count” the chromosomes even though the feature varies in size or geometry.

There is a concern that the interaction between the harmless precursor and the source feature, such as the end of the telomere, will interfere with cell division, injuring or killing normal healthy cells. A few comments.

The source feature is envisioned as acting like a catalyst with respect to the harmless precursor, such as:

(A(BC)) + SOURCE ==>((A(BC)(SOURCE))* ==> A + (BC) + SOURCE

The source feature is unchanged after the interaction just like a conventional catalyst. (A(BC)) is engineered in a meta-stable state so that it transforms into a harmless fragment (A) and the cell killer (BC) when it interacts with the source feature (SOURCE).

If the concentration of the harmless precursor (A(BC)) is relatively low, the source feature will be free and clear most of the time. Cell division may proceed safely. If the concentration is high enough, the source feature may be in the intermediate catalytic state ((A(BC)(SOURCE))* most of the time which may interfere with cell division — hopefully not, but it is a serious concern.

Ideally, the source and drain features will be chosen not to interfere with cell division.

To simplify the presentation of the basic concept, I have shown the source and drain features as static and unchanging during the complex cell division process. In reality, the chromosomes divide, replicate, and reorganize during cell division. A drain or source feature may be dynamic, appearing and disappearing with time. It may be possible to identify source or drain features that only exist when the cell is not dividing.

A few comments on the possible response of the body’s immune system to the pseudo-bacteriophage, which injects the drain feature into the cells.

It would be much better to find a naturally occurring drain feature that is constant in both normal cells and cancer cells. This would avoid developing the relatively complicated pseudo-bacteriophage mechanism altogether.

It may be possible to suppress any adverse immune reaction during the treatment by using immunosuppressive drugs such as cyclosporin that have proven successful in preventing organ transplant rejection. The treatment would be limited in duration unlike an organ transplant which is a lifetime condition. The treatment is for a terminal disease, cancer, where it seems reasonable to risk suppressing the immune system for a period of time.

The pseudo-bacteriophage is not a true infectious virus. It only injects a single drain into each cell. The drain is either a string of protein units or a string of non-coding DNA. The drain does not contain the genetic instructions to create additional bacteriophages. It does not take over the machinery of the cell and compell it to make more pseudo-bacteriophages.

In a true viral infection, the cell breaks down the viral proteins into peptides which are then expressed on the exterior surface of the cell where the immune system cells can find them and trigger a reaction to the unexpected “antigens” from the viral infection. This hopefully will not occur with the pseudo-bacteriophage.

The immune system may react to the pseudo-bacteriophages circulating in the blood and tissue outside the cells, just as it reacts to larger bacteria. To avoid this, it may be possible to coat the pseudo-bacteriophage with the naturally occuring antigens (about 5 nanometers in size, the bacteriophage is about 200 nanometers long) that identify the normal healthy cells in the body to the immune system.

A comment on another objection that I received. Again, the article intentionally omits many details and technical difficulties to present the basic concept simply and clearly.

Most cells in the human body have the normal twenty-three (23) pairs of chromosomes (a total of 46 chromosomes). However, there are some cells that do not have the normal number of chromosomes. Red blood cells have no chromosomes at all. Sperm and ova have half the normal number of chromosomes. In addition, there are a few types of cells such as some skeletal muscle cells that have multiple nuclei. That is, each nucleus has the normal forty-six chromosomes. However, the cell has more than one nucleus. These cells present potential problems for the practical implementation of the bathtub mechanism; obviously, we do not want to kill the red blood cells.

There is at least one potential fix for this problem which is to engineer pseudo-bacteriophages that only inject high-throughput drains into the few special types of cells with different numbers of chromosomes than forty-six. These pseudo-bacteriophages would inject special, high-throughput drains into these cells to ensure there is no buildup of toxin in these cells: red blood cells, skeletal muscle cells, and the few others. These special cells with non-standard numbers of chromosomes are rarely cancerous; we are most concerned with killing common kinds of cancer such as prostate cancer, breast cancer, and other types. These additional pseudo-bacteriophages obviously complicate the practical implementation of the bathtub mechanism.

If we can find a naturally occurring constant feature in the nucleus of cells (the drain when killing cells with too many chromosomes and the source when killing cells with too few chromosomes), then the problem will not occur.

Since red blood cells have no chromosomes, we don’t have to worry about killing the red blood cells when killing cells with too many chromsomes; there are no chromosomes to generate the toxin. The red blood cells will not perish during the “kill cells with too few chromosomes” phase because there is no constant source feature either.

The cells with multiple nuclei will have the right number of constant features (drains/sources) to balance the chromosomes (sources/drains).

The overall goal is to find a simple, easy to implement version of the bathtub mechanism. These special fixes to handle cells like red blood cells that do not have the normal number of chromosomes are a starting point. Hopefully, a more elegant solution can be found.

This animation illustrates a pseudo-bacteriophage injecting a super-drain only into a healthy cell such as a red blood cell that does not have forty-six chromosomes. The pseudo-bacteriophage uses surface cell receptors unique to this cell type, indicated by the cyan spheres on the cell membrane, to target the unusual cell. The super-drain removes the active cell killer from the healthy cell only. The Bathtub Mechanism will still kill the cancer cells with an abnormal number of chromosomes.

The relationship between cancer and aneuploidy is not well understood. For the purpose of the successful treatment or cure of cancer, whether aneuploidy is a cause or consequence of cancer may be an academic question. If we can find a feature that is always or frequently present in cancer cells or even predictably associated with highly malignant cancer cells and never or rarely present in normal cells, this feature can be used to selectively kill cancer cells or, at least, highly malignant cancer cells, curing or effectively treating the disease.

If cancer has a single unified cause, it is logical to seek this single cause. If cancer has many specific causes, it may be more effective to seek some common trait shared by the many variants of cancer, something that is a consequence rather than a cause.

Penicillin and many other antibiotics are effective because they attack a feature shared by the many different bacteria that cause bacterial pneumonias and other diseases, even though the specific causes of bacterial pneumonia and other diseases are many different kinds of bacteria — which differ at the genetic level.

The association of chromosomal abnormalities with cancer—including chromosome translocations, deletions, amplifications, and inappropriate numbers of chromosomes (aneuploidy)—has been known for more than a century. Even karyotypically stable cancers are genetically abnormal because of high frequencies of point mutations. Despite our current understanding of cancer genomes, it has been difficult to determine whether many genetic abnormalities are a cause or consequence of carcinogenesis. Increased missegregation of whole chromosomes prior to the final steps of cell division (mitosis) generates aneuploidy and can promote tumorigenesis in some genetic contexts in mice (1), as the German biologist Theodor Boveri initially proposed more than 100 years ago. Two papers in this issue, by Sheltzer et al. (2) on page 1026 and Solomon et al. (3) on page 1039, show that aneuploidy enhances genetic recombination and defective DNA damage repair, thereby providing a mechanistic link between aneuploidy and genomic instability.

Aneuploidy is the condition in which a cell has extra or missing chromosomes, and is often associated with tumours. But whether it is a cause or a consequence of cancer remains a vexed question.

Aneuploid cancers are like Tolstoy’s unhappy families: each aneuploid cancer has its own particular abnormal chromosome content, and thus its own abnormal characteristics. This variability has long frustrated biologists trying to establish whether aneuploidy is a cause or a consequence of malignant transformation.

Numeric aberrations in chromosomes, referred to as aneuploidy, is commonly observed in human cancer. Whether aneuploidy is a cause or consequence of cancer has long been debated. Three lines of evidence now make a compelling case for aneuploidy being a discrete chromosome mutation event that contributes to malignant transformation and progression process. First, precise assay of chromosome aneuploidy in several primary tumors with in situ hybridization and comparative genomic hybridization techniques have revealed that specific chromosome aneusomies correlate with distinct tumor phenotypes. Second, aneuploid tumor cell lines and in vitro transformed rodent cells have been reported to display an elevated rate of chromosome instability, thereby indicating that aneuploidy is a dynamic chromosome mutation event associated with transformation of cells. Third, and most important, a number of mitotic genes regulating chromosome segregation have been found mutated in human cancer cells, implicating such mutations in induction of aneuploidy in tumors. Some of these gene mutations, possibly allowing unequal segregations of chromosomes, also cause tumorigenic transformation of cells in vitro. In this review, the recent publications investigating aneuploidy in human cancers, rate of chromosome instability in aneuploidy tumor cells, and genes implicated in regulating chromosome segregation found mutated in cancer cells are discussed.

The relationship between aneuploidy and cancer remains unclear. Below, I discuss the effectiveness of attacking aneuploidy using the Bathtub Mechanism for different relationships between aneuploidy and cancer. I discuss ways to adapt the mechanism to work for the more difficult relationships, for example when only some cancer cells in a tumor are aneuploid and aneuploidy is not consistently associated with increased malignancy. The final entry in the list below discusses how to use even this uncooperative relationship between aneuploidy and cancer to cure or treat cancer.

Aneuploidy Causes Cancer

If aneuploidy is the cause of cancer or particular cancers, then a mechanism that selectively kills cells with an abnormal number of chromosomes (aneuploidy) and spares all or most normal cells with forty-six chromosomes as well as the few special types of normal cells such as red blood cells that do not have forty-six chromosomes, can probably cure cancer or the types of cancer caused by aneuploidy.

Aneuploidy is a Certain Consequence of Cancer

If aneuploidy is a certain consequence or side-effect of cancer or particular cancers, then a mechanism that selectively kills aneuploid cells and spares all or most normal cells with forty-six chromosomes as well as the few special types of aneuploid normal cells such as red blood cells, can probably cure cancer or the types of cancer caused by aneuploidy.

Aneuploidy is the Cause or Consequence of Greater Malignancy

If aneuploidy is the cause or consequence of greater malignancy in cancer or particular cancers, then a mechanism that selectively kills aneuploid cells and spares all or most normal cells with forty-six chromosomes as well as the few aneuploid normal cells such as red blood cells, can probably treat cancer or the types of cancer caused by aneuploidy, slowing or even arresting the disease. It probably cannot cure the disease entirely by itself.

Aneuploidy is the Cause or Consequence of Genetic Instability
(A Special Case of Greater Malignancy)

If aneuploidy is the cause or certain consequence of the genetic instability and rapid mutation in cancer or particular cancers that enables the cancers to develop immunity to anti-cancer drugs, then a mechanism that selectively kills aneuploid cells and spares all or most normal cells with forty-six chromosomes as well as the few aneuploid normal cells such as red blood cells, can probably cure cancer or the types of cancer caused by aneuploidy when combined with those anti-cancer drugs.

Once the rapidly mutating and adapting aneuploid cells are removed from the cancer, the remaining cells will often be unable to adapt to the anti-cancer drug as is now thought to occur. The failure of many anti-cancer drugs ranging from traditional chemotherapy agents to new genetic treatments such as Gleevec is frequently blamed on the rapid mutation and adaptation of the cancer cells. The drug works at first and then the cancer becomes immune and kills the patient.

Aneuploidy is Frequently Present.
A Marker for Tumors, but Not Individual Cancer Cells

If aneuploidy is frequently present in a population of cancer cells, for example ten percent of cells in a tumor are aneuploid, then it may be possible to adapt the Bathtub Mechanism to kill the tumors. The Bathtub Mechanism outlined in the article above is designed only to kill individual cells with an abnormal number of chromosomes.

When the aneuploid cells disintegrate, this introduces the poison into the surrounding tissue, but the concentration may be too low to kill even the neighboring cells by design. Recall that the cell killer (BC) is designed to be a weak poison that is not harmful to healthy cells at low concentration. It must build up to a high concentration in the aneuploid cells to kill the cells.

Even the basic Bathtub Mechanism may be able to introduce toxic levels of (BC) in the immediate vicinity of the aneuploid cells, killing its immediate neighbors. Thus, if aneuploidy is very common in a cancer, the non-aneuploid cancer cells will all have immediate aneuploid neighbors. The Bathtub Mechanism, properly engineered, will kill the entire cancer, both aneuploid and non-aneuploid cells.

What if aneuploid cells are less common in a tumor?

The toxic effect from each aneuploid cells must spread far enough from the aneuploid cells in the tumor to kill all the non-aneuploid cancer cells near the aneuploid cell which acts as a marker for the tumor — but no further, sparing the healthy tissue beyond. We can engineer this by adding a harmless precuror (DX) to a powerful toxin (X) to the system. This precursor is unable to enter the cells, unlike the cell-killer precursor (A(BC)) in the original system. The precursor (DX) is designed to break apart when it encounters the active cell killer (BC), producing the active toxin (X):

(DX) + (BC) ==> D + X + B + C

Note, that in this reaction, the cell killer (BC) is not a catalyst. It is consumed by reacting with the harmless precursor DX. Thus, the poison X is produced only within a range of the disintegrated aneuploid cancer cells. The poison X, more toxic than the cell-killer (BC), will then kill the neighboring cells in the tumor.

Why is this a possible cure?

In most cancers, the primary tumor does not kill the patient. It often can be surgically removed. For example, skin cancer can almost always be removed by surgery. However, the cancer becomes metastatic and forms secondary tumors in vital organs such as the lungs or liver where surgery is impossible. These secondary tumors eventually kill the patient.

Thus, we need some way to selectively destroy the metastatic tumors in the vital organs without destroying the healthy tissue around the tumors. One way would be a hypothetical tiny robot that enters the vital organ and methodically destroys the tumors and the tumors alone, perhaps under the control of a physician. This may one day be possible. At the moment, and probably for decades to come, it is beyond the capabilities of so-called nanotechnology.

The Bathtub Mechanism is not a robot. It is a much simpler system of molecules or molecular building blocks (such as the pseudo-bacteriophage). While it would be difficult to implement with current or near-future technology, it probably could be implemented. As a system of molecules it may avoid the many difficulties with inserting a tiny robot into the vital organs as well.

Conclusion

Aneuploidy is closely associated with cancer. This has been known for over a century and is not considered controversial. For the goal of curing or effectively treating cancer, it is not important whether aneuploidy is a cause or consequence of cancer.

The relationship between aneuploidy and cancer is not clear. While there are relationships between aneuploidy and cancer for which the author has not yet found a way to exploit aneuploidy to cure or treat cancer, in many cases it may be possible to exploit aneuploidy successfully, even when aneuploidy is not present in every cancer cell.

The author is not a biologist. Clearly, it would take experts in several fields of biology and organic chemistry (as well as applied mathematicians) to successfully implement the Bathtub Mechanism or some other, similar mechanism to selectively kill cells with an abnormal number of chromsomes. With some thought, specialists in these areas should also be able to see ways around some of the problems that may remain with the basic concept or find more elegant solutions to some of the problems than those suggested by the author.

At a given temperature, body temperature in this case, it would take a certain average amount of time (a few microseconds?) to process each molecule. The sources and drains would have a maximum throughput in number of molecules per second independent of the size of the cell at a constant temperature. In a larger cell, it would take longer for the concentration of the cell killer (BC) to build up to the toxic level when the drain was maxed out in aneuploid cells.

Technically, the molecules at a given temperature have a certain distribution of energies, something like the Maxwell-Boltzmann distribution. Temperature is loosely a measure of the average energy of the molecules in the distribution.

We might expect the more energetic molecules in the distribution to be processed faster than the less energetic molecules. However, at a given temperature, there should be a certain predictable maximum rate for the sources and drains. So long as we can average over enough molecules, the bathtub mechanism should function just the same as one would expect if there was a fixed time to process each molecule, e.g. one microsecond per molecule independent of energy.

If the patients have lost their ability to maintain constant body temperature for some reason, it might be necessary to use heating and cooling devices to artificially maintain a constant body temperature. Ideally, we would like to design the reactions so that they would work in patients suffering from chills or fevers as well as those with normal body temperature. Since the rates increase or decrease with temperature in both the sources and drains, this may well be possible.

I am not an organic chemist. An organic chemist might qualify this simple model of catalysis. To actually implement the bathtub mechanism successfully would require specific expertise in a number of fields such as organic chemistry. However, to develop the basic concepts for multi-disciplinary approaches of this type, it is necessary to venture out of one’s specific field of expertise.

I received some responses indicating that some readers may think the Bathtub Mechanism requires a different drug for each chromosome in the cell, so at least 23 chromosome types in a normal person and therefore at least 23 drugs.

I envision the harmless precursor interacting with a feature such as the telomeres that is common to all chromosomes.

It is even possible the Bathtub Mechanism could be implemented with a single drug/molecule.

If the drain feature which converts the active cell killer, poison, to harmless fragments is a naturally occurring feature of the cell, not something added as in my example, then the implementation would actually be a single drug — also requiring that the drain be properly multiplied in the healthy polyploid or aneuploid-like cells (megakaryocytes, some muscle skeletal muscle cells etc..) so the drug does not kill these healthy cells

However, I have never found a possible naturally occurring drain feature that would be certain to not be duplicated or changed in cancer cells, hence the more complicated scheme in the article using the modified bacteriophage to insert an artificial drain into the cells.